Relationship between Neumann solutions for two-phase Lame-Clapeyron-Stefan problems with convective and temperature boundary conditions

TL;DR

This paper establishes a relationship between Neumann solutions for two-phase Lame-Clapeyron-Stefan problems with different boundary conditions, providing inequalities that ensure the validity of classical solutions for phase-change materials.

Contribution

It derives conditions under which temperature and convective boundary solutions are equivalent in two-phase Stefan problems, extending previous results to more general boundary conditions.

Findings

Derived inequalities for convective transfer coefficients.

Established equivalence between boundary conditions under certain inequalities.

Reproduced classical results as special cases.

Abstract

We obtain for the two-phase Lam\'e-Clapeyron-Stefan problem for a semi-infinite material an equivalence between the temperature and convective boundary conditions at the fixed face in the case that an inequality for the convective transfer coefficient is satisfied. Moreover, an inequality for the coefficient which characterizes the solid-liquid interface of the classical Neumann solution is also obtained. This inequality must be satisfied for data of any phase-change material, and as a consequence the result given in Tarzia, Quart. Appl. Math., 39 (1981), 491-497 is also recovered when a heat flux condition was imposed at the fixed face.